The key to the MHD is that Monty knows where the car is and is bound by the rules of the game to show the goat. As a result, Monty's move tells the player nothing the player did not already know - viz., that there was at least one more door with a goat behind it.

I believe we want to go with the 50/50 chance because we are programmed to believe that intentional communication provides USEFUL information. Otherwise, why was it offered? The 50/50 "instinct" follows from the ingrained belief that Monty's action provides some assistance. That it doesn't provide useful information runs counter to how we move in the world.

If Monty does not know which door has the goat, and he randomly opens the door that HAPPENS to have a goat, that IS useful information, and there is then no benefit in switching. The chance that both you AND Monty have picked goats is as great as the chance that you picked the car originally, so it's a wash - or something like that.

To make an informed choice, the player must know that Monty will NOT be providing useful information. If the player doesn't know what rules Monty follows, there is a chance that Monty didn't know where the goat was, which changes the odds. But switching makes sense UNLESS the player knows that Monty's move is random, so, if the player is unsure of the rules, the player should switch.